Finite Group Databasebeta

← #15759572

Subgroups — #15759572

Order 3328.

410 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125987C211yesmaximal, characteristic
2#13123776C211yesmaximal, characteristic
3#13113517C211yesmaximal, characteristic
4#13113399C211yesmaximal, characteristic
5#13112694C211yesmaximal, characteristic
6#13112667C211yesmaximal, characteristic
7C13×#1993C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×C13×#97C2211yescharacteristic
11C13×#382C2211yescharacteristic
12#11718763—21no—
13#11718762—21no—
14#11718754C412yescomplemented
15#11718752—22no—
16#11718739C412yescomplemented
17#11718631—22no—
18#11718586C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718585C2211yescharacteristic
21#11718362—22no—
22#11718362—22no—
23C13×#340—21no—
24C13×#340—21no—
25#11718138—22no—
26#11718044—22no—
27C22×Q8×C13—21no—
28C22×C8×C13D411yescharacteristic
29C22×C8×C13D411yescharacteristic
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8C2×C412yes—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C42×C13C2311yescharacteristic
38#88180—21no—
39#88178—21no—
40#88178D412yes—
41C2×#6099—21no—
42#88124—21no—
43#88123C2×C411yescharacteristic
44#88123C2×C411yescharacteristic
45C4×Dic26—21no—
46C4×Dic26D412yes—
47C13×#97—21no—
48C13×#97—21no—
49C13×#95—21no—
50C13×#95—21no—
51C22⋊#1055—21no—
52C22⋊#1055—21no—
53#88055—22no—
54#88054—24no—
55C8×Dic13—22no—
56#88050—24no—
57#88047—24no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055D412yes—
62C4×#1055—21no—
63C4×#1055C2×C412yes—
64#9288—131nomaximal, Sylow
65C2×Q8×C13—22no—
66C2×Q8×C13—41no—
67C2×Q8×C13—82no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13#4111yescharacteristic
73C2×Dic26—21no—
74C2×Dic26C22⋊C412yes—
75C2×C8×C13—21no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13Q1612yes—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C42×C13C22×C411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13C2×D411yescharacteristic
90C42×C13#4111yescharacteristic
91C22⋊Dic13—22no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C22⋊C412yes—
96#6101—22no—
97#6101—22no—
98C4×Dic13—22no—
99#6099—41no—
100#6099—41no—
101C2×#1055—22no—
102C2×#1055—22no—
103C2×#1055—41no—
104#3230—131no—
105#2961—131no—
106#1993D1311yescharacteristic
107#1548—131no—
108#1518—131no—
109#1286—131no—
110#1275—131no—
111C23×C13#12111yescharacteristic
112Q8×C13—82no—
113Q8×C13—82no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—82no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13—81no—
121C2×C4×C13C2×C22⋊C411yescharacteristic
122C2×C4×C13C4×D411yescharacteristic
123C2×C4×C13C4×D411yescharacteristic
124C2×C4×C13#12011yescharacteristic
125C2×C4×C13#12111yescharacteristic
126C2×C4×C13#12311yescharacteristic
127C2×C4×C13C2×Q1611yescharacteristic
128C2×C4×C13#13511yescharacteristic
129C2×C4×C13#13711yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×Dic13—22no—
132C2×Dic13—22no—
133Dic26—42no—
134Dic26—81no—
135C8×C13—22no—
136C8×C13—41no—
137#1055—42no—
138#1055—42no—
139#1055—81no—
140#533—131no—
141C2×C4⋊Q8C2×D1311yescharacteristic
142#500—132no—
143#487—132no—
144#484—262no—
145#477—262no—
146#446—262no—
147#446—262no—
148#431—131no—
149#431—131no—
150#424—261no—
151#423—131no—
152#405—261no—
153C2×#97C2×D1311yescharacteristic
154#382C2×D1311yescharacteristic
155#340—21no—
156#340—21no—
157#333—262no—
158#328—262no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13#38611yescharacteristic
162C22×C13#46211yescharacteristic
163C22×C13#46411yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—82no—
169C4×C13—161no—
170C4×C13C4×Q1611yescharacteristic
171C4×C13#44111yescharacteristic
172C4×C13#45111yescharacteristic
173C4×C13#45211yescharacteristic
174Dic13—42no—
175Dic13—42no—
176C22×Q8—21no—
177C2×M16—261no—
178C22×C8C22⋊D1311yescharacteristic
179C22×C8C22⋊D1311yescharacteristic
180C4⋊Q8—21no—
181C4⋊Q8—21no—
182C4⋊Q8—21no—
183C4⋊Q8—131no—
184C4⋊Q8—131no—
185C4⋊Q8C4×D1312yes—
186#125—261no—
187C22⋊Q8—132no—
188C22⋊Q8—261no—
189C4×Q8—132no—
190C4×Q8—261no—
191#117—261no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C42C22×D1311yescharacteristic
196#107—264no—
197C4⋊C8—132no—
198C4⋊C8—264no—
199C4⋊C8—261no—
200C4⋊C8—261no—
201C4⋊C8—261no—
202#103—264no—
203C22⋊C8—261no—
204C22⋊C8—261no—
205#97—21no—
206#97—21no—
207#97—262no—
208C4×C8—132no—
209C4×C8—262no—
210C4×C8—261no—
211#95—21no—
212#95—21no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13#187811yescharacteristic
216C2×C13#190311yescharacteristic
217C2×C13#190911yescharacteristic
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—82no—
221C2×Q8—132no—
222C2×Q8—261no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4D4×D1311yescharacteristic
226C22×C4#612911yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228M16—521no—
229M16—521no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—262no—
236C2×C8—262no—
237C2×C8—521no—
238C2×C8#610712yes—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—132no—
246C4⋊C4—261no—
247C4⋊C4—262no—
248C4⋊C4—262no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C22⋊C4—262no—
252C42—262no—
253C42C2×C4×D1311yescharacteristic
254C42#612711yescharacteristic
255C42D4×D1311yescharacteristic
256C42D4×D1311yescharacteristic
257C13#928811yescharacteristic, complemented, Sylow
258C23#8819211yescharacteristic
259Q8—82no—
260Q8—82no—
261Q8—522no—
262Q8—1041no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—262no—
271C2×C4—262no—
272C2×C4C22⋊C4×D1311yescharacteristic
273C2×C4#8813511yescharacteristic
274C2×C4#8813711yescharacteristic
275C2×C4#8813811yescharacteristic
276C2×C4C4×C22⋊D1311yescharacteristic
277C2×C4#8819111yescharacteristic
278C2×C4#8819611yescharacteristic
279C2×C4C2×#610711yescharacteristic
280C2×C4#8820411yescharacteristic
281C2×C4#8820511yescharacteristic
282C8—22no—
283C8—41no—
284C8—522no—
285C8—522no—
286C8—1041no—
287C22—21no—
288C22—21no—
289C22#1171861711yescharacteristic
290C22#1171871511yescharacteristic
291C22#1171875111yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—82no—
297C4—161no—
298C4—522no—
299C4—522no—
300C4C4×#610711yescharacteristic
301C4#1171869111yescharacteristic
302C4#1171870811yescharacteristic
303C4#1171871111yescharacteristic
304C2—21no—
305C2—21no—
306C2#1311518011yescharacteristic
307C2#1311531311yescharacteristic
308C2#1311535511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1993C2
socleC22×C13#386
prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1993D13
hypocenterC13#9288
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1993

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
14. #11718754C4semidirect
16. #11718739C4semidirect
257. C13#9288semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131259872
#131237762
#131135172
#131133992
#131126942
#131126672
C13×#19932
#928813